Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

sample202.0ms

Algorithm

intervals

Results

127.0ms	112×	body	1280	valid
47.0ms	70×	body	640	valid
11.0ms	24×	body	320	valid
5.0ms	42×	body	80	valid
2.0ms	8×	body	160	valid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5171	26

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.1b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
16×	`unpow-prod-down_binary64`
10×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 102

Calls

4 calls:

17.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
15.0ms	(pow.f64 (sin.f64 ky) 2)
15.0ms	(pow.f64 (sin.f64 kx) 2)
95.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify66.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5014	2298

prune127.0ms

Filtered

67 candidates to 114 candidates (-70.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 3.4b

Counts

115 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac_binary64`
150×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
65×	`sqrt-prod_binary64`
32×	`unpow-prod-down_binary64`
28×	`associate-/r*_binary64`
26×	`distribute-lft-out_binary64`
17×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`div-exp_binary64`
6×	`pow-unpow_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rec-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 189

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
15.0ms	(pow.f64 (sin.f64 ky) 2)
15.0ms	(pow.f64 (sin.f64 kx) 2)
90.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify153.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4985	5648
1	4985	5648

prune148.0ms

Filtered

89 candidates to 201 candidates (-125.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	201	11	212

Merged error: 3.4b

Counts

212 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
0.3b	(pow.f64 (sin.f64 kx) 2)
4.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

1005×	`times-frac_binary64`
608×	`*-un-lft-identity_binary64`
437×	`add-sqr-sqrt_binary64`
436×	`add-cube-cbrt_binary64`
215×	`sqrt-prod_binary64`
92×	`unpow-prod-down_binary64`
86×	`distribute-lft-out_binary64`
46×	`add-exp-log_binary64` `div-inv_binary64`
32×	`div-exp_binary64`
30×	`associate-/l*_binary64` `sqrt-div_binary64`
29×	`associate-/r/_binary64`
16×	`add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
13×	`associate-/r*_binary64`
8×	`1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 518

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2)
28.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (sin.f64 ky) 2)
164.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
15.0ms	(pow.f64 (sin.f64 kx) 2)
98.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify244.0ms

Algorithm

egg-herbie

Counts

530 → 530

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5227	22008

prune368.0ms

Filtered

172 candidates to 530 candidates (-208.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	528	2	530
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	530	11	541

Merged error: 3.4b

Counts

541 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.8b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
45×	`sqrt-prod_binary64`
41×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
18×	`unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
10×	`pow1_binary64`
8×	`add-exp-log_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `unswap-sqr_binary64`
3×	`associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
19.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (sin.f64 ky) 2)
15.0ms	(pow.f64 (sin.f64 kx) 2)
171.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
149.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

simplify90.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4947	2375
1	4947	2375

prune98.0ms

Filtered

73 candidates to 127 candidates (-74.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 3.4b

Counts

138 → 11

regimes194.0ms

Accuracy

0% (1.3b remaining)

Error of 4.0b against oracle of 2.7b and baseline of 4.0b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	29
1	20	29

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.3s	3779×	body	1280	valid
1.4s	2016×	body	640	valid
346.0ms	724×	body	320	valid
166.0ms	1197×	body	80	valid
99.0ms	284×	body	160	valid

Details

analyze1.3s

sample202.0ms

simplify106.0ms

prune2.0ms

localize15.0ms

rewrite34.0ms

series296.0ms

simplify66.0ms

prune127.0ms

localize16.0ms

rewrite43.0ms

series285.0ms

simplify153.0ms

prune148.0ms

localize17.0ms

rewrite91.0ms

series292.0ms

simplify244.0ms

prune368.0ms

localize19.0ms

rewrite41.0ms

series351.0ms

simplify90.0ms

prune98.0ms

regimes194.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample6.6s

Profiling